probability

A and B plays chess everyday . The probability that A beats B in any game is twice the probability that B beats A . The probability that B beats A is three times the probability that the game ends in a draw . What is the probability that the game ends in a draw ?

A and B plays chess everyday . The probability that A beats B in any game is twice the probability that B beats A . The probability that B beats A is three times the probability that the game ends in a draw . What is the probability that the game ends in a draw ?

My working :
P(A wins ) = 2(1- P(A wins ))
P(A wins ) = 2/3

P(B wins) is not equal to 1- P(A wins). This is because you have to also consider the possibility of a draw.